Homework 4

Continue reading Chapter 1 in the Kamen/Heck text. In particular, read sections 1.1 and 1.5 carefully, and browse sections 1.2, 1.3, and 1.4. On Friday, we will discuss signals, systems, continuous-time versus discrete-time, and the classification of systems as linear and time-invariant and causal.

Bode plots: Please study the Homework 3 solutions, and try to construct the Bode plot on your own. In order to get more practice constructing Bode plots, please construct the magnitude and phase plots for the following circuit. On your magnitude plot, label the -3 dB cutoff frequency, the gain of the filter in the passband, and the slope of the "roll-off" in the stopband.

[CIRCUIT DIAGRAM OMITTED IN HTML VERSION]

This exercise will provide practice converting between amplitude gain and decibels (dB). Consider a sine wave with amplitude 1 volt that is passed through 7 filters. The filter gains at the sine wave frequency are as follows:

0 dB, 3 dB, 6 dB -3 dB, 20 dB, -20 dB, and - 40 dB

What is the amplitude (in volts) of the output sine wave from each filter?

Classify each filter on the back of this page as low-pass, high-pass, or band-pass. You can do this by looking at each filter as a voltage divider, and determining the behavior of each impedance in the circuit for low frequencies, middle frequencies, and high frequencies. Alternatively, you can write the equation for the frequency response and study its behavior as the frequency varies.

[CIRCUIT DIAGRAM OMITTED IN HTML VERSION]

For the low-pass filters:
Is one of them "closer" to an ideal filter than the others?
Please explain.